Demonstrating the properties of rotations, if a line segment with endpoints (0,−3)

Question

(
0
,
−
3
)
and (0,−7)
(
0
,
−
7
)
is rotated 90°
90
°
clockwise, what is an endpoint of this rotated segment?(1 point)
Responses

(−3, 0)
(
−
3
,

0
)
left parenthesis negative 3 comma 0 right parenthesis

(0, 3)
(
0
,

3
)
left parenthesis 0 comma 3 right parenthesis

(0, 7)
(
0
,

7
)
left parenthesis 0 comma 7 right parenthesis

(3, 0)

Answer 1

To rotate a point \((x, y)\) 90° clockwise around the origin, we use the transformation:

\[ (x, y) \rightarrow (y, -x) \]

Now, let's find the coordinates for both endpoints of the line segment:

1. Rotating the endpoint \((0, -3)\):

   • Applying the transformation: \((0, -3) \rightarrow (-3, 0)\)

2. Rotating the endpoint \((0, -7)\):

   • Applying the transformation: \((0, -7) \rightarrow (-7, 0)\)

Thus, the endpoints of the rotated segment will be \((-3, 0)\) and \((-7, 0)\).

Since the question asks for one of the endpoints after rotation, for the correct answer:

The rotated endpoint of (0, -3) is (−3, 0).

Therefore, the correct response is:

\[ \text{(−3, 0)} \]